Find the RADIUS OF THE CIRCLE

Can you calculate the radius of a circle that is enclosed by a larger square, along with a smaller square? Test your math skills and solve this interesting geometry problem!

This video will guide you through the steps to calculate the radius of the circle. Perfect for students learning about geometry and shapes, as well as anyone who enjoys solving math puzzles.

By the end of this video, you’ll learn how to calculate the radius of the circle by applying key geometry concepts and principles.

If you love math challenges and want to improve your geometry skills, this video is for you! Don’t forget to like, comment, and subscribe for more exciting math and geometry tutorials.

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[davidseed]

r+r/sqrt2=3
r(1+1/sqrt2)=3
r( sqrt2+1)/sqrt2 =3
At this stage you should rationalise the denominator

r= 3( 2-sqrt2)
r = 6-3sqrt2

[AkantorJojo]

Isn't it easier to caöcuöate using the fact taht the circle in question is the "in-circle" of the triangle created when using the diagonal of the big square running from the bottom left to the top right?
Using that fact we can use the formula for the radius of the in-circle that uses just the area and sircumference of the triangle in question; both of witch are relatively easy to calculate.
Using said methor my result comes yout as "\frac{6}{2 + \sqrt{2}}" wich is the same as yours - after some algebra manipulation - but arguably prittyer ;) .

[martinfurtner]

Once again, two similar triangles make life easy and the solution fast. Use r right away, no need for further unknown variables, nor trigonometric functions.😀

3 : sqr(18) = (6 - r) : (sqr(18) + r) and after a little algebra r =sqr(18) : (1 + sqr(2)) = 1, 7574

[nathanoy_]

In my opinion the shortest way to calculate this problem is with the height or width:
3 = r + r * sin45° => r = 3/(1+sin45°)
one liner, easy to follow, fast to calculate

[guusbouman]

but what are the coordinates of the midpoint?